Solution: The LCM of 143 and 51 is 7293
Methods
How to find the LCM of 143 and 51 using Prime Factorization
One way to find the LCM of 143 and 51 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 143?
What are the Factors of 51?
Here is the prime factorization of 143:
1
1
1
×
1
3
1
11^1 × 13^1
1 1 1 × 1 3 1
And this is the prime factorization of 51:
3
1
×
1
7
1
3^1 × 17^1
3 1 × 1 7 1
When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 11, 13, 3, 17
3
1
×
1
1
1
×
1
3
1
×
1
7
1
=
7293
3^1 × 11^1 × 13^1 × 17^1 = 7293
3 1 × 1 1 1 × 1 3 1 × 1 7 1 = 7293
Through this we see that the LCM of 143 and 51 is 7293.
How to Find the LCM of 143 and 51 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 143 and 51 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.
Let’s take a look at the multiples for each of these numbers, 143 and 51:
What are the Multiples of 143?
What are the Multiples of 51?
Let’s take a look at the first 10 multiples for each of these numbers, 143 and 51:
First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430
First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510
You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 143 and 51 are 7293, 14586, 21879. Because 7293 is the smallest, it is the least common multiple.
The LCM of 143 and 51 is 7293.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 44 and 150?
What is the LCM of 26 and 136?
What is the LCM of 12 and 133?
What is the LCM of 124 and 98?
What is the LCM of 38 and 126?